where d⁢(P,O)dPOd(P,\,O)means the distance of the pointPPP of the branch from the origin and
d⁢(P,l)dPld(P,\,l) the distance of PPP from the line lll.

Examples: The hyperbolax2a2-y2b2=1superscriptx2superscripta2superscripty2superscriptb21\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 has the asymptotes y=±ba⁢xyplus-or-minusbaxy=\pm\frac{b}{a}x; the curvey=sin⁡xxyxxy=\frac{\sin x}{x} the asymptote y=0y0y=0.